Low-Rank Adaptation (LoRA) is a popular technique for efficient fine-tuning of foundation models. However, applying LoRA in federated learning environments, where data is distributed across multiple clients, presents unique challenges. Existing methods rely on traditional federated averaging of LoRA adapters, resulting in inexact updates. To address this, we propose Federated Exact LoRA, or FedEx-LoRA, which adds a residual error term to the pre-trained frozen weight matrix. Our approach achieves exact updates with minimal computational and communication overhead, preserving LoRA’s efficiency. We evaluate the method on various models across arithmetic reasoning, commonsense reasoning, natural language understanding and natural language generation tasks, showing consistent performance gains over state-of-the-art methods across multiple settings. Through extensive analysis, we quantify that the deviations in updates from the ideal solution are significant, highlighting the need for exact aggregation. Our method’s simplicity, efficiency, and broad applicability position it as a promising solution for accurate and effective federated fine-tuning of foundation models.

The veracity of a factoid is largely independent of the language it is written in. However, language models are inconsistent in their ability to answer the same factual question across languages. This raises questions about how LLMs represent a given fact across languages. We explore multilingual factual knowledge through two aspects: the model’s ability to answer a query consistently across languages, and the ability to ”store” answers in a shared representation for several languages. We propose a methodology to measure the extent of representation sharing across languages by repurposing knowledge editing methods. We examine LLMs with various multilingual configurations using a new multilingual dataset. We reveal that high consistency does not necessarily imply shared representation, particularly for languages with different scripts. Moreover, we find that script similarity is a dominant factor in representation sharing. Finally, we observe that if LLMs could fully share knowledge across languages, their accuracy in their best-performing language could benefit an increase of up to 150% on average. These findings highlight the need for improved multilingual knowledge representation in LLMs and suggest a path for the development of more robust and consistent multilingual LLMs.